7.11.26 problem 26

Internal problem ID [347]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 26
Date solved : Wednesday, February 05, 2025 at 03:24:00 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=x \,{\mathrm e}^{3 x} \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 37

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+13*y(x)=x*exp(3*x)*sin(3*x),y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{3 x} \left (\sin \left (3 x \right ) x -5 \cos \left (2 x \right ) c_1 -5 \sin \left (2 x \right ) c_2 +\frac {6 \cos \left (3 x \right )}{5}\right )}{5} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 44

DSolve[D[y[x],{x,2}]-6*D[y[x],{x,1}]+13*y[x]==x*Exp[3*x]*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{25} e^{3 x} (-5 x \sin (3 x)-6 \cos (3 x)+25 c_2 \cos (2 x)+25 c_1 \sin (2 x)) \]